IM1B Final Exam!

Area Model / Distributive Property

100

(2x + 3)²

4x² + 12x + 9

200

(x - 2)(3x² + 3x +2)

3x³ - 3x² -4x -4 

300

(3x + 3)(3x - 3)

9x² - 9

400

(x - 4)(2x + 3)

2x² - 5x - 12

500

(3x +y⁴)²

9x² +6xy⁴ + y⁸

Rewriting, Looking Inside, Undoing

100

3√ (x-3) = 27

x = 84

200

^{x - 1}/₃ ^{+ x + 6}/₇ = -9

x = -20

300

(3x - 7)² = 81

x = ¹⁶/₃ or -²/₃

400

√(2x + 5) =10

X = 47.5

500

(x - 1)(x + 3) = (x + 1)(x - 7)

x = -¹/₂

Systems, Exponential Equations

100

4x - 3y =-13

-x + 6y = -44

y = -9

x = -10

200

-4x -4y = 24

3x + 10 = y

x = -4
y = -2

300

find the equation of the exponential graph y=ab^x through: (0,7) and (4,112)

y=(7)(2)^x

400

find the equation of the exponential graph y=ab^x through: (2, 0.36) and (4, 0.1296)

y=(1)(0.6)^x

500

find the equation of the exponential graph y=ab^x through: (-1, 1.25) and (3, 0.032)

y = (0.5)(0.4)^x

Inequalities and Explicit Equations

100

Find boundary points and write answer as an inequality:
^x-2/₅ + 2 ≥ x

2  ≥ x

200

Find boundary points and write answer as an inequality:
^3x/₄ + ^2x/₂ < 16

x < ⁶⁴/₇

300

Write an explicit equation for:

-8, 1, 10, ...

t(n) = 9n -17

400

Write an explicit equation for:
25, 5, 1, ...

t(n) = 125 (¹/₅)ⁿ

500

Write an explicit equation for:
3, ³/₂,³/₄

t(n)=6(¹/₂)ⁿ

Surprise!

100

What was Mr. Procsal's high school's mascot?

Pumas!

200

Vincent invested $390 into an account paying 2.7% interest compounded daily. How much money will he have in 18 years?

$524.86

300

Given the linear function f(x)=3x - 3 describe the transformation for f(x) + 7.

shift up 7.

400

write an equation for the combined functions m(x)-n(x):
m(x) = 7x - 6

n(x) = x² + 5

-x² + 7x -11

500

-3y³⋅y²⋅ y^{-3
____________}
-4y^-4⋅ y³

3y³

^___

⁴